CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
UNIVERSITY OF COLORADO AT DENVER
TITLE: A Framework for Variational Grid Generation with Matrix Norms
SPEAKER: Patrick M. Knupp, Ecodynamics Research Associates, Albuquerque, NM
DATE: Friday, February 23, 1996
PLACE: Math Conference Room - Suite 540
UCD Building, 1250 14th St., Denver
TIME: noon - 1 pm
ABSTRACT
A general approach to the construction of functionals to be used for
variational grid generation of structured grids, in which the Jacobian matrix
and matrix norms play a central role, is introduced. The theory focuses on
the Jacobian matrix because all first-order geometric properties of a
structured grid---including the direction of coordinate lines---are represented
by this matrix. If directional control is not needed, the metric tensor
can be used in place of the Jacobian matrix. We show how grids with
desired properties can be generated by minimizing functionals that require
combinations of weight matrices with the Jacobian matrix or metric tensor to
take certain basic forms. Most of the well-known grid generators fit within
this framework, and new ones, which directly control the Jacobian matrix,
are proposed. The first part of the talk will be a brief introduction to
structured grid generation, largely based on the book `The Fundamentals of
Grid Generation' by myself and Stanly Steinberg.